Related papers: Balanced matrices
A hermitian matrix can be parametrized by a set consisting of its determinant and the eigenvalues of its submatrices. We established a group of equations which connect these variables with the mixing parameters of diagonalization. These…
Relying on recent advances in statistical estimation of covariance distances based on random matrix theory, this article proposes an improved covariance and precision matrix estimation for a wide family of metrics. The method is shown to…
Matrix concentration inequalities and their recently discovered sharp counterparts provide powerful tools to bound the spectrum of random matrices whose entries are linear functions of independent random variables. However, in many…
In a graph A, for each two arbitrary vertices g, h with d(g,h)=2,|MAg2h|=mAg2h is introduced the number of edges of A that are closer to g than to h. We say A is a 2-edge distance-balanced graph if we have mAg2h=mAh2g. In this article, we…
A new determinant inequality of positive semidefinite matrices is discovered and proved by us. This new inequality is useful for attacking and solving a variety of optimization problems arising from the design of wireless communication…
An $n\times n$ matrix is said to have a self-interlacing spectrum if its eigenvalues $\lambda_k$, $k=1,\ldots,n$, are distributed as follows $$ \lambda_1>-\lambda_2>\lambda_3>\cdots>(-1)^{n-1}\lambda_n>0. $$ A method for constructing sign…
A modeling methodology and matrix formalism is presented that permits analysis of arbitrarily complex interferometric waveguide systems, including polarization and backreflection effects. Considerable improvement results from separation of…
This paper has an expository nature. We compare the spectral properties (such as boundedness and compactness) of three families of semi-infinite matrices and point out similarities between them. The common feature of these families is that…
In this paper we explore a class of equivalence relations over $\N^\ast$ from which is constructed a sequence of symetric matrices related to the Mertens function. From numerical experimentations we suggest a conjecture, about the growth of…
This paper is concerned with the spectral properties of matrices associated with linear filters for the estimation of the underlying trend of a time series. The interest lies in the fact that the eigenvectors can be interpreted as the…
The main goal of this article is to present new types of inequalities refining and reversing inequalities of the harmonic mean of scalars and matrices. Furthermore, implementing the spectral decomposition of positive matrices, we present a…
Structural balance is an important characteristic of graphs/networks where edges can be positive or negative, with direct impact on the study of real-world complex systems. When a network is not structurally balanced, it is important to…
The concept of sequency holds a fundamental significance in signal analysis using Walsh basis functions. In this study, we closely examine the concept of sequency and explore the properties of sequency-complete and sequency-ordered…
The diagonalization of matrices may be the top priority in the application of modern physics. In this paper, we numerically demonstrate that, for real symmetric random matrices with non-positive off-diagonal elements, a universal scaling…
We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…
We characterize the eigenvalues and eigenvectors of a class of complex valued tridiagonal $n$ by $n$ matrices subject to arbitrary boundary conditions, i.e. with arbitrary elements on the first and last rows of the matrix. %By boundary…
We investigate the properties of positive definite and positive semi-definite symmetric matrices within the framework of symmetrized tropical algebra, an extension of tropical algebra adapted to ordered valued fields. We focus on the…
To better understand the algebra $\mathcal{M}_n$ of all $n\times n$ complex matrices, we explore the class of accretive matrices. This class has received renowned attention in recent years due to its role in complementing those results…
We study the functions that count matrices of given rank over a finite field with specified positions equal to zero. We show that these matrices are $q$-analogues of permutations with certain restricted values. We obtain a simple closed…
In this work we use matrix models to study the problem of strength distributions. This is motivated by noticing near exponential fall offs of strengths in calculated magnetic dipole excitations. We emphasize that the quality of the…